To summarise, going back to Diagrams (REF ) and (REF ), [1]} starts with \(T\)  and then, on the one hand define \(L\)  via \(LB=\mathsf {P}T\mathsf {S}B\)  on finite \(\mathbf {BA}\) s and, on the other hand, define \(L^{\prime }\)  via \(L^{\prime }A=\mathsf {P}^{\prime }T^{\prime }\mathsf {S^{\prime }}A\)  on finite \(\mathbf {DL}\) s with \(T^{\prime }\)  the posetification of \(T\) .
